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Theory and Modern Applications

Table 1 Spatial convergence rates in \({L_{2}}\) and temporal rates

From: Fourth-order finite difference scheme and efficient algorithm for nonlinear fractional Schrödinger equations

α

1/h

1/τ

\(\|u-u_{h}\|_{L_{2}}\)

Spatial rate

Temporal rate

1.3

24

28

2.6919e-6

  

25

210

2.2419e-7

3.5858

1.7929

26

212

2.4566e-8

3.1899

1.5949

27

214

1.8398e-9

3.7390

1.8695

1.9

24

28

1.0250e-5

  

25

210

9.3139e-7

3.4601

1.7300

26

212

5.5518e-8

4.0683

2.0341

27

214

2.9951e-9

4.2122

2.1050